Question

(sin 5x + sin 3x) / (cos 5x + cos 3x) का हल होगा

tan 2x

tan 6x

tan 4x

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Answer 1

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$\frac{sin5x + sin3x}{cos5x + cos3x} \\ = \frac{2sin( \frac{5x + 3x}{2})cos( \frac{5x - 3x}{2} ) }{2cos( \frac{5x + 3x}{2})cos( \frac{5x - 3x}{2}) } \\ = \frac{sin4x}{cos4x} \\ = tan4x$

Answer 2

Option 3) tan 4x is the correct answer ✔️

Formula used :

$sin \: x+ sin \: y = 2 \: sin( \frac{x + y}{2} )cos (\frac{x - y}{2} )$

$cos \: x + cos \: y = 2 \: cos( \frac{x + y}{2} )cos( \frac{x - y}{2} )$

$tan \: x = \frac{sin \: x}{cos \: x}$

Refer the attachment for complete answer ✔️